Related papers: Regularity conditions for solutions to some parabo…
A by now classical result due to DiBenedetto states that the spatial gradient of solutions to the parabolic $p$-Laplacian system is locally H\"older continuous in the interior. However, the boundary regularity is not yet well understood. In…
In this paper, we study the backward problem of determining initial condition for some class of nonlinear parabolic equations in multidimensional domain where data are given under random noise. This problem is ill-posed, i.e., the solution…
We consider degenerate and singular parabolic equations with $p$-Laplacian structure in bounded nonsmooth domains when the right-hand side is a signed Radon measure with finite total mass. We develop a new tool that allows global regularity…
In this paper there are estimated the derivatives of the solution of an initial boundary value problem for a nonlinear uniformly parabolic equation in the interior with the total variation of the boundary data and the L^{infinity}-norm of…
We establish partial regularity for vector-valued solutions to parabolic systems where the coefficients are possibly discontinuous with respect to (x,t). More precisely, we assume a VMO-condition with respect to the (x,t) and continuity…
In this paper we present the following result on regularity of solutions of the second order parabolic equation $\partial_t u - \mbox{div} (A \nabla u)+B\cdot \nabla u=0$ on cylindrical domains of the form $\Omega=\mathcal O\times\mathbb R$…
For systems of ordinary differential equations on a compact interval, we study the character of solvability of the most general linear boundary-value problems in Sobolev spaces. We find the indices of these problems and obtain a criterion…
In this paper we prove higher regularity for 2m-th order parabolic equations with general boundary conditions. This is a kind of maximal L_p-L_q regularity with differentiability, i.e. the main theorem is isomorphism between the solution…
In the present paper, we establish sharp Sobolev estimates for solutions of fully nonlinear parabolic equations, under minimal, asymptotic, assumptions on the governing operator. In particular, we prove that solutions are in…
An initial-boundary value problem for the 3D Zakharov-Kuznetsov equation posed on bounded domains is considered. Existence and uniqueness of a global regular solution as well as exponential decay of the $H^2$-norm for small initial data are…
This paper is concerned with the regularity of solutions to linear and nonlinear evolution equations extending our findings in [22] to domains of polyhedral type. In particular, we study the smoothness in the specific scale…
It is shown that globally positive solutions of a linear second order parabolic partial differential equation on a bounded domain, with Dirichlet boundary conditions, are unique up to multiplication by a positive constant.
The Dirichlet problem for a class of stochastic partial differential equations is studied in Sobolev spaces. The existence and uniqueness result is proved under certain compatibility conditions that ensure the finiteness of…
This note presents a regularity result with proof for an initial-boundary value problem of a linear parabolic system involving curl of the unknown vector field, subjected to the boundary condition of prescribing the tangential component of…
We establish existence and uniqueness of generalized solutions to the initial-boundary value problem corresponding to an Euler-Bernoulli beam model from mechanics. The governing partial differential equation is of order four and involves…
We investigate the regularity of linear stochastic parabolic equations with zero Dirichlet boundary condition on bounded Lipschitz domains $O \subset R^d$ with both theoretical and numerical purpose. We use N.V. Krylov's framework of…
Motivated by problems arising in geometric flows, we prove several regularity results for systems of local and nonlocal equations, adapting to the parabolic case a neat argument due to Caffarelli. The geometric motivation of this work comes…
The aim of this work is studding the behavior of solutions of initial boundary problem for degenerated nonlinear parabolic equation of the second order, conditions of existence and non-existence in whole by time solutions, is establish.
We study a general discrete boundary value problem in Sobolev--Slobodetskii spaces in a plane quadrant and reduce it to a system of integral equations. We show a solvability of the system for a small size of discreteness starting from a…
In this paper, we study the Sobolev regularity of solutions to nonlinear second order elliptic equations with super-linear first-order terms on Riemannian manifolds, complemented with Neumann boundary conditions, when the source term of the…